Frank Lampard’s side found themselves three goals behind at the break after goals from Kevin De Bruyne, Phil Foden and Ilkay Gundogan.
City dominated the half and could have added a fourth and fifth if they had their shooting boots on, with Chelsea looked particularly shaky at the back against a rotated Pep Guardiola side.
Though City’s first half performance drew praise from Neville, the former United skipper said Chelsea’s lacklustre midfield were partly to blame.
‘I have to say the midfield of Kante, Mount and Kovacic have been nowhere near good enough,’ Neville told Sky Sports.
‘It’s been nowhere near good enough in this last 20 minutes. They’ve allowed Manchester City to get a real grip in this game.
‘The full backs of Chilwell and Azpilicueta have really struggled but it’s that midfield that has really struggled to get a grip.’
Despite a string of below-par individual performances, Lampard resisted the urge to make changes at half-time.
City continued their domination in the second half and they could have added to their lead with Gundogan and De Bruyne passing up further opportunities.
Callum Hudson-Odoi was a late entry into the game and he grabbed a consolation with practically the last kick off the game.
The defeat against City means Chelsea have won just one of their last seven matches in all competitions.